Debye screening of static chromoelectric fields at high temperature is
investigated at next-to-leading order through one-loop resummed pertu
rbation theory. At this order the gluon propagator appears to give ris
e to strong deviations from a Yukawa form of screening. Generally, an
oscillatory behavior is found which asymptotically becomes repulsive,
but in a gauge-dependent manner. However, these features are strongly
sensitive to the existence of screening of static magnetic fields. It
is shown that a small magnetic screening mass can restore exponential
screening with a gauge-independent value of the screening mass, which
depends logarithmically on the magnitude of the magnetic mass. Recent
results obtained in temporal axial gauge, which instead indicate an as
ymptotic (repulsive) power-law behaviour of screening, are also critic
ally discussed. In order to arrive at a gauge-invariant treatment of c
hromoelectric screening, Polyakov loop correlations are considered, bo
th with and without dynamical gauge symmetry breaking. Again a crucial
sensitivity to the scale of magnetic screening is found. A detailed c
omparison of the perturbative results with recent high-precision latti
ce simulations of the SU(2) Polyakov loop correlator is made, which ar
e found to agree well with the perturbative result in the symmetric ph
ase when a magnetic mass similar to g(2)T/4 is included.